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Friday, June 27, 2014

Check the Y-axis when reading a chart

Here is an interesting way to make statistics more persuasive without
really lying.

Take a look at this chart. It was labeled "Hospital
readmissions sharply declined."

Now look at this one. The same data are charted, but the
decline does not look nearly as sharp.

A common trick is to abbreviate the Y-axis of a chart. Proponents
of this will tell you it makes the chart more compact and easier to read.
However, the downside is that a small change is made to appear much larger.

Even though the change was said to be statistically significant in this
instance, the casual reader would certainly be impressed much more by the sharp
decline depicted in the first chart.

I believe the first chart was produced by the Centers for
Medicare and Medicaid Services (CMS) to show that its policy on readmissions
was working. I was unable to find the original source for it.

This also works with other graphics as shown in this pair of
bar charts from the Visualizing
Data blog.

I encourage you to look for this type of manipulation when you read research papers. pharmaceutical ads, or any other depiction of data.

First convert all the data to percentages. Then, sum those percentages. Do this for two selected periods (like Q4 of 2013 vs. Q4 of 2014).Now calculate the overall percentage reduction between the two quarters (in this case, it was a drop from 5% to 4%).Round up the number, to make it sound a bit more impressive, and announce it proudly! As in:

An interesting variation on this theme is scaling a figure according to some measure. For example, if you showed a 30% bigger dollar sign to indicate a 30% increase in revenue. The area of the sign would be 69% rather than 30% bigger, thus making the increase seem larger.

Sceptical Scalpel, sadly no. This was internal data, and therefore I cannot point you to a publication. Saying the name of the firm out loud wouldn't be too smart either, given that I work there (still).